active and passive filters
DESCRIPTION
Learn to design basic filters and butterworth filtersTRANSCRIPT
www.ku.edu.npDepartment of Electrical & Electronics Engineering www.ku.edu.np/ee
EEEG 213: Network AnalysisLecture-22: Filters
SHAILENDRA KUMAR JHADepartment of Electrical & Electronics EngineeringKathmandu University, Dhulikhel
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Outline• Definition of Filters• Frequency filters• Types of frequency filters• Active filters design
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References:
1. Boylestad R. L., Introductory Circuit Analysis, PHI, 1999
2. Gayakwad R. A., “Op-Amps and Linear Integrated Circuits”, PHI,1998
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Definition
A network designed to either block orpass energy
– Amplitude filters– Frequency filters
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Frequency filtersA network designed to select or reject aband of frequencies
Types:– Analog and digital– Passive or active– Low pass, high pass, band pass and band
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• Analog filters are designed to processanalog signals
• Digital filters process analog signals usingdigital techniques
• Passive filters are designed usingresistors, inductors and capacitors
• Active filters employ transistors or op-amps in addition with resistors,inductors and capacitors
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Low Pass filters
• Allows only low frequency to pass• has constant gain from 0Hz to a high
cutt-off frequency fH
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Pass band stop band
Ideal response
fHfrequency
Gain (Vo/Vi)
1
0
real response
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High Pass filters
• Allows only high frequency to pass• has constant gain after cutt-off
frequency fL
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Stop band pass band
Ideal response
fLfrequency
Gain (Vo/Vi)
1
0
real response
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Band Pass filters• Designed to pass certain band of frequencies while
rejecting all frequencies below and above this range.
• has constant gain between two cut-off frequencies fLand fH
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Ideal response
fLfrequency
Gain (Vo/Vi)
1
0 fH
Passband
stop bandStopband
real response
fC
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Band Stop filters• Designed to reject certain band of frequencies while
pass all frequencies below and above this range.
• has constant gain from 0Hz to low cut of frequencyfL and after high cut-off frequencies fH
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Ideal response
stopband
pass bandpassband
fLfrequency
Gain (Vo/Vi)
1
0 fH
real response
fC
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Real filter designs• Butterworth filters
– Flat pass band as well as stop band– Roll of 20dB/decade/pole– Used when all frequencies in pass band must have
same gain
• Chebyshev filters– Ripple pass band and flat stop band– Sharper cut-off than Butterworth– Roll of greater than 20dB/decade/pole– Use when rapid roll of required
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Real filter designs
• Cauer filters– Ripple pass band and ripple stop band– Gives the best stop band response– Even sharper cut-off than Chebyshev
• Bessel filters– Linear response i.e no distortion in pass band– Roll off rate less than 20dB/decade/pole– Used for filtering pulse waveform without
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Stop Band
Real filter designs
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frequency
GainButterworthChebyshevCauerBessel
Pass Band
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Low Pass RC filter
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At any intermediate frequency, the output voltage Vo isgiven as
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For frequency less than fc will result in an output voltage Vo that isat least 70.7% of the maximum.
For any frequency above fc, the output is less than 70.7% of theapplied signal.
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High Pass RC filter
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At any intermediate frequency, the output voltage Vo isgiven as
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Band Pass Filters
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Band Stop Filters
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Filters and roll of ratesThe number of poles determines the roll-off rate
First order - one pole - roll-off of -20dB/decade
Second order- two poles-roll-off of -40dB/decade
Third order - three poles-roll-off of -60dB/decade
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First Order Low Pass Butterworth Filter
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R1 Rf
R
C RL
VO
Vi
+15V
-15V
V1
= −−According to voltage divider rule,
, = 1 +And output voltage = (1 + )
That is = (1 + ) 1 + = 1 + ( )
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Where, == 1 + =f = frequency of the input signal= 12 =The gain magnitude and phase angle equations of thelow-pass filter can be written as= 1 + ( )And ∅ = − ( )
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At very low frequency, that is f < fH=At f = fH,
At f > fH
Thus the low-pass filter has a constant gain AF from 0Hz to -the high cutoff frequency fH.
At fH the gain is 0.707Af and after fH it decreases at aconstant rate with an increase in frequency.
The frequency f = fH is called the cutoff frequency becausethe gain of the filter at this frequency is down by 3 dB (= 20log 0.707) from 0 Hz.
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= 2 = 0.707<
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A low-pass filter can be designed by implementingthe following steps:
1. Choose a value of high cutoff frequency fH
2. Select a value of C less than or equal to 1F.Mylar or tantalum capacitors arerecommended for better performance.
3. Calculate the value of R using
4. Finally select values of R, and RF dependent onthe desired pass band gain AF using
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= 12= 1 +
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Frequency ScalingThe procedure used to convert an original cutofffrequency fH to a new cutoff frequency f’H is calledfrequency scaling.
• To change a high cutoff frequency multiply R or C,but not both, by the ratio of the original cutofffrequency to the new cutoff frequency.
• In filter design the needed values of R and C areoften not standard. Besides, a variable capacitor C isnot commonly used.
• Therefore, choose a standard value of capacitor,and then calculate the value of resistor for a desiredcutoff frequency. This is because for a nonstandardvalue of resistor a potentiometer can be used.
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… problems …
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Second Order Low Pass Butterworth Filter
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R2
R1 Rf
R3
C3RL
VO
Vi
+15V
-15VC2
The voltage gain magnitude is = ( )A = 1 + RR = pass band gain of the filterf = frequency of the input signal= 1/2π R R C C= high cutoff frequency of the filter
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Except for having twice the roll-off rate in the stop band, thefrequency response of the second-order low-pass filter is identicalto that of the first-order type.
The design steps of the second-order filter are:
1. Choose a value of high cutoff frequency fH
2. To simplify the design calculations, set R2=R3=R and C2=C3=C.then choose a value of C less than or equal to 1F.
3. Calculate the value of R using
4.Because of the equal resistor R2=R3 and capacitorC2=C3, the pass band voltage gain AF of the second-order low- pass filter has to be equal to 1.586.• That is, RF = 0.586R1.• This gain is required for Butterworth response.Hence choose a value of R1 100k and calculate thevalue of RF.
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= 12
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… problems …
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First Order High Pass Butterworth FilterR1 Rf
C
RRL
VO
Vi
+15V
-15V
For a first order high pass filter, the output voltage is= (1 + ) 1 += [ ]
Where, = 1 + =f = frequency of the input signal= 12 =
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The magnitude of the voltage gain is
Since high-pass filters are formed fromlow-pass filters simply by interchangingR's and C's, the design and frequencyscaling procedures of the low-pass filtersare also applicable to the high-passfilters.
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= ( )1 + ( )
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… problems …
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Second Order High Pass Butterworth Filter
C2
R1 Rf
C3
R3
RL
VO
Vi
+15V
-15VR2
The magnitude of the voltage gain is= 1 + ( )Where Af = 1.586 for second order Butterworth reponse
f = frequency of the input signal (Hz)fL = low cutoff frequency (Hz)
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…problems…
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Band Pass Filter
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R’1 R’f
R’
C’ RL
VO
+15V
-15V
R1 Rf
C
RVi
+15V
-15V
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Band Reject Filter
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R’1 R’f
R’
C’
+15V
-15V
R1 Rf
C
R
Vi
+15V
-15V
R2 R4
R3
ROM
RL
VO
+15V
-15V
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Notch filter
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